As far as I know, stakes in the United States don't have their own tax ID numbers. The Church has a generic federal tax ID number (EIN) that applies to all units in the United States. You can find the Church EIN on your donor statement, which is available through the LDS.org Online Donations tool, and the EIN will be on the top-right corner of the statement.

Thanks for the help. I called the Church tax administration at 801-240-3003. They gave me a number that appears to be specific to my stake; or at least it's not the same as the number I've seen posted around that is supposed to apply to all US units.